How do you use the product rule to find the derivative of #y=x^2*sin(x)# ?

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Answer 1 · 2018-03-23T04:13:13

#y'=x(2sinx+xcosx)#

The Product Rule tells us that if we have two functions #f(x), g(x),# multiplied by one another, then

#(fg)'=fg'+gf'#

Here, for #y=x^2sinx,# we see #f(x)=x^2, g(x)=sinx#

Thus,

#y'=sinxd/dxx^2+x^2d/dxsinx#

#y'=2xsinx+x^2cosx#

Factor out #x# to simplify:

#y'=x(2sinx+xcosx)#